Computer Science 1 Top Lectures Assignments Noticeboard Designing loops

Reading: Chapter 9.1-9.3.11

• Like designing classes, there is a method for defining loops that can be helpful
• Informal procedure
• Choosing and defining variables
• The while sketch
• The while condition
• Initialization
• Guaranteeing termination
• Completing the loop body
• Initialization (again)

Multiplication

private int multiply (int x, int y) {...}

Informal procedure

• Observe that multiplication is just repeated addition
x * y = 0 + x + x + x + ... + x        x added to 0, y times
• Note: using 0 so that multiplication works for the case that y is 0
• So, informal procedure is:
• start with 0 and add x to it, then add x to the result, then add x to that result, until we've added it y times. The last result is the value to return

Choosing and defining variables

• Need to keep track of the result, and the number of additions so far. This suggests two variables:

int count; // count == the number of additions done
int result; // result == 0 + x + x + ... + x, i.e., result == x * count

Skeleton of the code

private int multiply (int x, int y) {
  int count; // count == the number of additions done
  int result; // result == 0 + x + x + ... + x, i.e., result == x * count

  ...
  while (condition) {
    body
  }
  ...

}

The while condition

• count contains the number of additions so far; thus, at the end of the loop we want count == y.
• we therefore want to continue the loop as long as count is not equal to y
• at the end of the loop, result will contain the value we wish to return

while (count != y) {
  body
}
//count == y, result == x * y
return result;

Initialization

• according to our design so far, count contains the number of times that we have added so far
• before the loop has executed once, this is 0, so count should be 0

Guaranteeing termination

• So far, the while statement we have written will not terminate
• In the loop body, we need to increment count by 1 each time through the loop
• This makes sense because
• one more time through the loop means one more addition
• count will move closer to y the next time around

while (count != y) {
  rest of body
  count += 1;
}

Completing the loop body

• Our loop design tells us that count should be the number of times x has been added.
• each time we increment count, we should add x to the result again

while (count != y) {
  result += x;
  count += 1;
}

Initialization again

• We have initialized count, and x and y are arguments to multiply method
• What about result?
• Loop design says that result == x * count.
• If count is 0 (at beginning of loop), we have done no addition, so result should be intialized to 0.
• This makes sense also from our design which says that result = 0 + x + x + ... + x

private int multiply (int x, int y) {
  int count; // count == the number of additions done
  int result; // result == 0 + x + x + ... + x, i.e., result == x * count

  count = 0;
  result = 0;
  while (count != y) {
    result += x;
    count += 1;
  }
  return result;

}